Symposium CT06—From Quantum Mechanics to Materials Engineering—Recent Progress on the Development and Novel Applications of Ab Initio Methods in Materials Science

I will discuss the theory and practice of Koopmans spectral functionals, aiming to reproduce total energies and spectra of molecules and materials with functional formulations. A comparison many-body perturbation theory is provided for ionization potentials and electron affinities of molecules and band structures of solids, showing an agrement with experiments comparable to the current state-of-the-art, and at a fraction of the computational costs. I will illustrate also the implementation in open-source periodic-boundary condition codes. Work done in collaboration with Nicola Colonna, Riccardo de Gennario, Edward Linscott, Linh Nguyen, and Andrea Ferretti.

One important approach for the description of quantum many-body systems is to design functionals: observables or effective potentials are expressed in terms of relatively simple quantities, such as the density or a one-body Green’s function, instead of calculating expectation values with many-body wavefunctions. However, although efficient approximations for such functionals exist for some important observables, such as the total energy, they still lack precision for many applications, and other observables cannot be accessed in a satisfactory way. For example, Density Functional Theory (DFT) and Time-Dependent (TD) DFT still face major difficulties to describe strongly correlated systems, or excitonic effects in optical spectra. For other observables, even less is known about how to build good density functionals.
One way of designing approximations is to use results of model systems. In this talk we will show how model results can be used in an in principle exact way, called “Connector Theory”, in order to describe observables and systems of interest. Within this approach, a quantity of interest is calculated for a model system as function of a parameter once and forever, and the results are stored. Under certain conditions, the result for an appropriate choice of parameter can then be used to replace a value of interest in a given real system. This choice of parameter is called “connector”.
We will discuss the principles and general properties of such an approach. Of course, in practice, the connector has to be approximated. We will show that formulating the problem in this way is a convenient starting point for approximations, and a strategy to build systematic approximations will be presented. Some discussion and results can be found in [1,2].

[1] M. Vanzini, A. Aouina, M. Panholzer, M. Gatti, and L. Reining, arXiv:1903.07930v3
[2] M Panholzer, M Gatti, L Reining; Phys. Rev. Lett. 120, 166402 (2018).

Raman spectroscopy is frequently used to identify composition, structure and layer thickness of 2D materials. Here, we describe an efficient first-principles workflow for calculating resonant first-order Raman spectra of solids within third-order perturbation theory employing a localized atomic orbital basis set. The method is used to obtain the Raman spectra of around 1000 different monolayers selected from the Computational 2D Materials Database (C2DB)[1]. On basis of this database, we propose an automatic procedure for identifying a material based on an input experimental Raman spectrum and demonstrate it for the cases of MoS₂ (H-phase) and WTe₂ (T′′-phase)[2]. Employing a similar computational methodology, we calculated nonlinear optical (NLO) spectra of about 400 non-centrosymmetric semiconducting monolayers. NLO phenomena such as harmonic generation, Kerr, and Pockels effects are of great technological importance for lasers, frequency converters, modulators, switches, etc. Recently, 2D materials have drawn significant attention due to their strong and unique NLO properties. Sorting the non-resonant nonlinearities of the monolayers with respect to bandgap E_gap reveals an upper limit proportional to E_gap^-4, which is neatly explained by a generic two-band model. We identify multiple promising candidates with giant nonlinearities and band gaps ranging from 0.4 to 5 eV, some of which approach the theoretical upper limit and greatly outperform known materials[3].
The comprehensive libraries of ab initio Raman and NLO spectra are freely available via the C2DB website(https://cmrdb.fysik.dtu.dk/c2db/).

References:
[1] The Computational 2D Materials Database: High-Throughput Modeling and Discovery of Atomically Thin Crystals, S. Haastrup et al., 2D Materials 5, 042002 (2018)
[2] A library of ab initio Raman spectra for automated identification of 2D materials, A. Taghizadeh et al, Nature Comm. 11, 3011 (2020)
[3] Two-dimensional Materials with Giant Optical Nonlinearities Near the Theoretical Upper Limit, A. Taghizadeh et al, arXiv:2010.11596

Intermetallic clathrate compounds have a huge compositional and configurational space that allows for tailoring their properties towards a high thermoelectric efficiency. Semiconducting behavior is often difficult to achieve due to the intricate interplay between electronic structure, temperature, and disorder. For instance, in the complex clathrate compound Ba₈Al_xSi_46-x, the configuration of the Al atoms in the crystal framework drastically affects the electronic behavior [1]. This is most strikingly the case at the technologically relevant composition × = 16, whose ordered ground state is semiconducting, while disordered structures at higher energies are metallic. We have developed a multi-scale approach, based on statistical thermodynamics combined with the cluster-expansion method [2] and ab initio calculations which allows us to calculate the temperature-dependent effective band structure of alloys without relying on effective medium approximations [3]. With its help, we discover a semiconductor-to-metal transition that is accompanied by an order-disorder phase transition at 582 K.
[1] M. Troppenz, S. Rigamonti, and C. Draxl, Chem. Mater. 29, 2414 (2017).
[2] S. Rigamonti, et al., CELL: python package for cluster expansions with a focus on complex alloys. URL: https://sol.physik.huberlin.de/cell
[3] M. Troppenz, S. Rigamonti, J. Sofo, and C. Draxl, https://arxiv.org/abs/2009.11137

In this talk I will present strategies to predict and design materials for next generation technologies by combining theories based on quantum mechanics, and algorithms and codes running on high performance classical computers, and, in some cases, on near-term quantum computers. I will specifically focus on predicting and designing materials to build radically novel sensors and computers, so as to move in earnest into the quantum information age.

The concept of optimal tuning (OT) of range-separated hybrid (RSH) functionals has become an important tool for overcoming the fundamental gap problem and the charge transfer excitation problem in molecular systems. Here, this concept is extended to the solid state by introducing dielectric screening and orbital localization into the functional form. This approach, couched rigorously within the generalized Kohn-Sham formalism of density functional theory, can produce quantitatively the same one and two quasi-particle excitation picture given by many-body perturbation theory (MBPT), without any empiricism. Specifically, for covalent/ionic semiconductors and insulators, accurate band structures and optical absorption spectra, which agree well with those obtained from MBPT, are obtained. For molecular solids, the approach predicts the correct gap renormalization - even from single molecule calculations if a polarizable continuum model is used in an electrostatically consistent manner – and also predicts absorption spectra well.

Single-photon superradiance arises when a collection of identical emitters are spatially separated by distances much less than the wavelength of the light they emit and results in the formation of a superradiant state that spontaneously emits light with a rate that scales linearly with the number of emitters. This collective phenomena has only been demonstrated in a few nanomaterial systems, none of which have used quasi-2D nanoplatelets as the emitter. In this work, we rationally design a single colloidal nanomaterial that hosts multiple (nearly) identical emitters. Specifically, by combining molecular dynamics, atomistic electronic structure calculations, and model Hamiltonians methods, we show that quasi-2D nanoplatelets oriented along each face of a “nanocuboid” can serve as the (nearly) identical emitters required to observe both superradiant and subradiant phenomena. Utilizing layer by layer growth techniques to synthesize a nanocuboid, we demonstrate single-photon superfluorescence via single-particle time-resolved photoluminescence measurements at room temperature. The realization of superradiant and subradiant states in these single nanocuboids opens the door to ultrafast single-photon emitters and may provide an avenue to entangled multi-photon states via superradiant cascades.

This work is partially supported by the Army Research Office MURI (Ab-Initio Solid-State Quantum Materials) under Grant No. W911NF-18-1-0431. JP is a Ziff Fellow at the Harvard University Center for the Environment.

The mathematical framework for classifying nanostructures shows that a vast class of such materials can be described as being helical, i.e., their spatial atomic arrangement possesses helical symmetries. Helical nanostructures include important technological materials such as nanotubes, nanowires, nanoribbons and nanosprings; miscellaneous chiral structures encountered in chemistry; and examples from biology, including tail sheaths of viruses and many common proteins. Helical nanostructures have received much attention recently due to their unusual and interesting material properties, including e.g., their strong association with ferromagnetism, ferroelectricity and superconductivity, unique transport characteristics, and the existence of strong coupling between their mechanical and optical/transport properties.

Given the relative abundance of helical nanostructures and their scientific and technological importance, there is a pressing need to have reliable and efficient computational tools for studying such structures. In this work, we will describe the formulation and implementation of a first principles simulation tool for helical nanostructures based on a symmetry adapted real space formulation of Kohn-Sham Density Functional Theory. Specifically, the computational method employs a finite difference discretization of the governing equations in so called helical coordinates, and handles symmetries arising from common helical groups by using an appropriate version of the Bloch theorem for such systems. This combination of features of the method allows one to simulate for example, the behavior of nanotubes of arbitrary chirality ab initio.

We utilize the newly developed computational tool to carry out a first principles study of various nanotubes. In particular, we will describe the behavior of group IV nanotubes under twisting deformations as revealed by our simulations. We will describe interpretation of some of the mechanical properties of these tubes, computed ab initio, from the perspective of elasticity theory. We will also highlight the interplay between mechanical strains and electronic states in these materials and comment on the effects of structural relaxation.

I will present recent developments in predicting electronic excitations using the combination of stochastic computational techniques and many-body theory. The methodology relies on operators' decomposition via random vectors and recasting expectation values as statistical estimators. In practice, the implementation of diagrammatic methods employs real-time and real-space sampling.[1] This formalism leads to substantial computational savings and reduced scaling with the number of electrons; it enables first-principles predictions of quasiparticle energies in systems with thousands of atoms. In detail, I will describe our recent work on simulating nanoscale condensed systems within the linear scaling stochastic GW approximation.[2,3,4] Further, I will show that statistical sampling of interactions is an efficient route to go beyond GW: I will detail our work on the stochastic GWΓ approach, which combines non-local vertex corrections in the screened Coulomb interaction and self-energy.[5] I will demonstrate that the vertex corrections affect unoccupied states, improve the quasiparticle energies, and capture multi-quasiparticle excitations otherwise missing in GW.[5,6] Despite the increased complexity of the self-energy, the stochastic GWΓ scales linearly with the system size.

[1] V Vlcek, W Li, R Baer, E Rabani, D Neuhauser, Physical Review B 98 (7), 075107 (2018)
[2] J Brooks, G Weng, S Taylor, V Vlcek, Journal of Physics: Condensed Matter 32 (23), 234001 (2020)
[3] G Weng, V Vlcek The Journal of Physical Chemistry Letters 11 (17), 7177-7183 (2020)
[4] M Romanova, V Vlcek The Journal of Chemical Physics 153 (13), 134103 (2020)
[5] V Vlcek, Journal of Chemical Theory and Computation 15 (11), 6254-6266 (2019)
[6] C Mejuto-Zaera, et al., arXiv preprint arXiv:2009.0240122020

First, we will present a new embedding approach [1] in the stochastic GW technique [2-4] that enables efficient treatment of the impurity states with high accuracy and minimal effort. The method is based on a partitioning of the Green’s function and screened Coulomb potential into the deterministic subspace (usually containing localized states) and the stochastic subspace (the rest of the Hilbert space). The enhanced stochastic-deterministic sampling minimizes statistical errors in energies of localized quasiparticles.
Further, we will present a new technique for the stochastic decomposition of the many-body interactions into additive subspace contributions. We partition the Hilbert space and compute the polarization self-energy via sampling selected charge density fluctuations in real space and time. The decomposition accounts for quasiparticle scattering by correlations from a particular subspace. We identify couplings among different areas (spatial or energetic), e.g., screening contributions in quantum interfaces.
We exemplify our approaches on N-vacancy defects in pristine monolayer and an hBN - graphene bilayer (> 2,000 electrons). We demonstrate the new hybrid stochastic-deterministic approach reduces statistical errors and leads to more than an order of magnitude savings in computational time. The computed subspace self-energy unveils how interfacial couplings affect electronic correlations and identifies contributions to excited-state lifetimes. While the embedding is necessary for the proper treatment of impurity states, the decomposition yields new physical insight into quantum phenomena in heterogeneous
systems.

1. M. Romanova, V. Vlcek, J. Chem. Phys. 153, 134103, 2020
2. D. Neuhauser et al., Phys. Rev. Lett. 2014, 113, 076402
3. V. Vlček et al., Phys. Rev. B 2018 , 98 , 075107
4. V. Vlček et al., J. Chem. Theory Comput. 2017 , 13 , 4997–5003.

This work was supported by the NSF MRSEC Program through Grant No. DMR-1720256 and by the UCSB NSF Quantum Foundry Q-AMASE-i, Award No. DMR-1906325.

Mixed-dimensional heterojunctions (MDHJ) comprised of 0D molecules deposited on 2D materials are actively being explored for opto-electronic applications. As a result of the extreme heterogeneity in the density of states and dielectric screening of these systems, properties of MDHJs are impacted by numerous distinct and competing energy scales, including local and non-local electronic correlations, interfacial dipole and orbital hybridization, which complicates theoretical description of MDHJs accurately. Here we analyze the electronic structure of 0D-2D (metallophthalocyanines-MoS₂) heterojunctions using multi-objective optimization of range-separated hybrid functionals that incorporates screened exact exchange for asymptotically-correct Coulomb potential. We obtain electronic structures consistent with experimental photoemission results in both energy level alignment and electronic band gaps, representing a significant advance compare to standard DFT methods. We elucidate MoS₂ valence resonance with the transition-metal phthalocyanine non-frontier 3d orbitals and how they contribute to emergent interfacial properties. This resonance is also highly dependent on the transition metal identity, enabling controlled tunability of the 0D/2D MDHJs. Based on our calculations, we derive parameter-free, model self-energy corrections to semi-local density functional theory for mixed-dimensional heterojunctions at different dielectric environment in an efficient way. In a broader context, these results illustrate how theory can impact the design and realization of precisely tailored mixed dimensional heterojunctions for specific opto-electronic functions.

Ab initio many-body perturbation theory methods, like GW and GW plus Bethe Salpeter Equation (GW-BSE), are well-established and highly-accurate techniques for calculating the quasiparticle and optical properties of moderate-sized systems. There remain, however, a number of challenges when it comes to scaling up these techniques to address systems with a large number of heterogeneous atoms, various forms of aperiodicity, and large energy scales well-outside the optical regime. In this talk, I will discuss our newly developed subspace embedding and downfolding techniques for GW-BSE calculations on low-dimensional and amorphous systems that exemplify these challenges. In particular, we apply GW-BSE to study optical properties of heterostructures of quasi two dimensional (quasi-2D) materials, as well as the effect of electron-hole interactions on core-level spectra of quasi-2D materials and amorphous water, including dynamic effects due to scattering to the electron-hole continuum. The calculations are made possible through a combination of physically motivated approximations and algorithms, including non-uniform spatial sampling, low-rank approximations, and subspace embedding and matrix downfolding techniques. We find that electron-hole interactions play an essential role in the scattering of core-level excitations with excitations from the valence band.

Hybrid functionals reduce the self-interaction error in semi-local density functional theory (DFT) and provide a semi-quantitative description of the electronic structure in systems throughout chemistry, physics, and materials science. However, the high computational cost associated with evaluating the exact exchange (EXX) interaction limits hybrid DFT from treating large-scale condensed-phase systems. To address this challenge, we have developed a linear-scaling real-space approach that exploits the sparsity in the EXX interaction using local orbitals (MLWFs). The resulting massively parallel algorithm (exx) provides an accurate evaluation of all EXX quantities and enables hybrid DFT based ab initio molecular dynamics (AIMD) of large-scale finite-gap systems with a wall time cost comparable to semi-local DFT [1]. Since exx was optimized to treat homogeneous systems, its performance degrades when treating highly anisotropic heterogeneous systems with multiple phases and/or components. In this work, we discuss three major theoretical and algorithmic advances that enable efficient and accurate hybrid DFT based AIMD of large-scale heterogeneous systems, and showcase the extended exx module when treating a complex solid-liquid interface.
[1] J Chem Theory Comput 16, 3757 (2020).

To date, due to the rapid progress in science and technology, the efforts for reaching new plasmonic materials are extensively growing. Although the most often used noble metals, such as Au and Ag, demonstrate a strong optical response in plasmonics and metamaterials, some of their inherent features make them less suitable for real-world applications. In this work, we aim to seek new alternative plasmonic materials by proposing a novel and reliable method via manipulating the characteristic response of candidate compounds such as Al/Ga doped Zinc Oxide (A/GZO), ZrN, TiN and Silicon allotropes. This method merges two powerful computational approaches, namely, density functional theory (DFT) and electromagnetic (EM) simulations by the finite-element method (FEM) and more rigorous methods (e.g. TMM, RCWA). We first perform a series of DFT calculations, including the structural relaxation of plasmonic material candidates, to find the crystal structure with minimum energy, for different exchange-correlation functionals such as GGA, LDA. In a second step, we analyse the simulated material’s electronic and optical properties to illustrate potential metallic behaviour, from the viewpoint of material science, via electronic density of states (DOS), band structure and optical dispersion functions (real and imaginary parts). To evaluate the found material’s performance in a semi-real plasmonic system, we subsequently extract the optical dispersion parameters, such as refractive index data as well as Drude-Lorentz parameters of complex dielectric permittivity from our calculated DFT. We finally feed the generated optical dispersion data into an EM-solver for optical simulations of any desired optical system and investigate its efficiency for suitability in plasmonic applications. Our method comprises the possibility for verification with experimental data on each level. From there on, we can optimize digitally the molecular structure, paving the way to predict the proposed compounds’ plasmonic functionality, overcoming the persistent hurdles introduced by pure experimental works.

We have developed the embedded cluster density approximation (ECDA) for scaling up high-level Kohn-Sham density functional theory (KS-DFT) calculations in large systems. ECDA is a local correlation method formulated in the framework of KS-DFT. In ECDA, a cluster is defined for each atom based on the density embedding theory. The cluster’s exchange-correlation (XC) energy density is then calculated using advanced, orbital-based XC functionals. The system's XC energy is obtained by patching clusters’ XC energy densities in an atom-by-atom manner. We have derived an efficient way to calculate the system’s XC potential, making ECDA fully self-consistent and suitable for studying charge reorganization in heterogeneous materials. ECDA is a variational method, and analytical forces have also been derived. Numerical examples show that ECDA can be applied to various systems that have different bond types, which makes ECDA a nearly black-box method.

Electron scattering on a non-trivial Fermi surface topology plays an important role in electron transport, thus giving rise to exotic phenomena such as violation of Wiedemann Franz law, hydrodynamic electron flow, unusual phonon decay etc. Recent experimental discoveries in axis-dependent conduction polarity, or goniopolarity, have observed that the charge carriers can conduct like either electrons or holes depending on the crystallographic direction they travel along in layered compounds such as NaSn2As2 and PdCoO2, the latter of which also features hydrodynamic electron flow. In this talk, we present an ab initio study of electron scattering in such systems. Taking NaSn2As2 as an example, we study different microscopic scattering mechanisms from ab initio and present the electron-phonon scattering time distribution on its Fermi surface in momentum space, the anisotropy of which is proposed to be the origin of the axis-dependent conduction polarity. Further, we obtain the overall anisotropic lifetime tensors in real space at different electron chemical potentials and temperatures and discuss how they contribute to the macroscopic thermopower. While we find that the contribution of the in-plane and cross plane lifetimes exhibits a similar trend, the concave portion of the Fermi surface alters the electron motion significantly in the presence of a magnetic field, thus flipping the conduction polarity as measured via the Hall effect. Our calculations and analysis of NaSn2As2 also suggests the strong possibility of hydrodynamic electron flow in the system. These results together have implications for electron lifetimes in a broad class of new quantum materials and provide key, general insights into electron scattering on open Fermi surfaces.

Electrons in condensed matter can flow collectively when their momentum is on-average conserved during microscopic scattering processes. This 'hydrodynamic' regime has been observed in graphene,^1-2 and more recently in bulk materials such as WTe2 at moderately low temperatures and micrometer lengthscales.^3-4 This enables direct observation of strong electron interactions otherwise challenging to measure. Competition between the ballistic, at low temperatures and nanometer lengthscales, and diffusive regimes, at high temperatures and millimeter lengthscales, suggests this phenomenon can only be observed in a narrow temperature/lengthscale window.

In this work, we compute temperature-resolved microscopic scattering rates for a broad range of materials, from first principles. We then utilize these, together with crystal symmetry constraints, to compute an effective viscosity tensor - which we use as a diagnostic tool for hydrodynamic material candidates.

Despite momentum conservation inside the material, electron scattering at the boundary lead to the unique spatial signatures, such as Poiseuille flow, observed in experiments.^1-4 We investigate the effect of nanoscale geometries on these viscous electron fluids by using two independent methods: i) Macroscopic solution of the electronic Navier Stokes equation using the ab-initio viscosity tensors computed above,⁵ ii) Microscopic solution of the spatially-resolved Boltzmann transport equation using the ab-initio scattering matrix.⁶

This works paves the path in experimentally-observable signatures of hydrodynamic electron flow based on first principles diagnostics.

¹ Sulpizio, J. A. et al. Nature 576, 75–79 (2019).
² Ku, M. et al. Nature 583 (2020)
³ de Jong, M. and Molenkamp, L., PRB 51 (1995)
⁴ Vool, U., Hamo, A., Varnavides, G., Yaxian, W. et al arXiv:2009.04477 (2020)
⁵ Varnavides, G., Jermyn, A.S., Anikeeva, P. et al. Nat Commun 11, 4710 (2020)
⁶ Varnavides G., Jermyn A.S., Anikeeva P. et al. Phys. Rev. B 100 115402 (2019)

The small-polaron hopping model has been used for several decades for modeling electronic charge transport in oxides. Despite its significance, the model was developed for binary oxides, and its accuracy has not been rigorously tested for higher-order oxides. To investigate this issue, we chose the Mn_xFe_3-xO₄ spinel system, which has exciting electrochemical and catalytic properties, and mixed cation oxidation states that enable us to examine the mechanisms of small-polaron transport. Using a combination of experimental results and DFT+U calculations, we find that the charge transport occurs only between like-cations (Fe/Fe or Mn/Mn). And due to asymmetric hopping barriers and formation energies, we find that the polaron is energetically preferred to the polaron, resulting in an asymmetric contribution of the Mn/Mn pathways.

Reference:
A. Bhargava, R. Eppstein, J. Sun, M. A. Smeaton, H. Paik, L. F. Kourkoutis, D. G. Scholm, M. Caspary Toroker*, R. D. Robinson*, “Breakdown of the small-polaron hopping model in higher-order spinels”, Adv. Mat., 2004490 (2020).

Silicon nanoparticles (Si-NPs) represent one of many types of nanomaterials, were the origin of emission is difficult to assess due to a complex interplay between the core and surface chemistry, especially due to silicon's strictly covalent chemistry. Band-gap tunability in ideal fully crystalline hydrogen capped Si-NPs is predicted to span from infrared to ultraviolet spectral range, but this is rarely observed in practice.

In this work, we simulate "fuzzy band structure", radiative rates and HOMO-LUMO energy (band-gap size) tunability of ~2nm Si-NPs. In particular we asses the role of surface, such as (i) covalently bonded atoms/molecules, (ii) strain and (iii) disorder. Simulations are done on the density functional theory level and compared with experimental results by a state-of-the-art single-dot correlative microscopy
tool. By this method, the size of the individual NPs is measured by an atomic force microscopy (AFM) and the optical band-gap is evaluated from a single-dot photoluminescence measured on the very same NPs. We propose that (a) covalently bonded species alter the overal energy levels and transition rates, (b) strain reduces the radiative rates and (c) disorder reduces the bandgap tunability range. Our observations might explain the often obsered puzzlingly fast radiative rates in organically capped Si-NPs and weak size tunability in most epxerimentally realized Si-NP systems.

Nowadays there are many attempts in the world of science to harness quantum mechanics. One of the widely explore fields with the potential of practical usage is the anti-Stokes emission phenomena. Obtained during the research gadolinium oxide nanoparticles doped with selected metals were used to investigate energy transfer between erbium (Er³⁺) and ytterbium (Yb³⁺) ions and enhance of the efficiency of anti-Stokes emission by doping structures with magnesium ions (Mg²⁺).

The examined materials were synthesized by a homogeneous precipitation method for 2 hours at a temperature of 85°C. The crystal structure arrangement was obtained by calcining at a temperature of 990°C for 3 hours. The nanoparticles were characterized with several methods. Size and form were analyzed by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The crystal structure was determined by X-ray diffraction (XRD). The atomic composition of the nanoparticles was characterized by energy-dispersive X-ray spectroscopy (EDS). Optical properties were analyzed by using photoluminescence measurements. Finally, nanoparticles were incubated with mouse mammary carcinoma (4T1) cells for 24h to examine their suitability for use in biology as luminescent markers.

As result, nanoparticles show luminescence in the visible region - emission maxima occur at a wavelength of 565 nm (⁴S_3/2 → ⁴I_15/2, ²H_11/2 → ⁴I_15/2) and 663 nm (⁴F_9/2 → ⁴I_15/2) during excitation with a semiconductor laser with a wavelength of 980 nm (continuous wave). An increase in the effectiveness of the anti-Stokes emission process was observed - an 8-fold increase in red luminescence efficiency was obtained for nanoparticles doped with 2.5% Mg²⁺ compared with non-doped nanoparticles (Gd₂O_3: 1% Er³⁺,18% Yb³⁺). The measurements were carried out at a laser power density of 12 W×cm^-2. The nanoparticles were dissolved in a dimethyl sulfoxide solution. The nanoparticles' diameter was 380 nm, 282 nm, and 260 nm (before calcining). The diameters of the obtained nanoparticles - are 302 ± 37 nm and 278 ± 36 nm (after a calcining) respectively.

Periodic, density functional theory calculations were employed to understand the hydrodechlorination of trichloroethylene (TCE) over different facets of a palladium catalyst. In order to accomplish this, the Pd surface was modelled as terrace sites (Pd(111)) and undercoordinated sites (Pd (211), Pd (100) and Pd (110)). The most stable binding configuration of TCE on the Pd surface was found to be through the di-σ mode of binding, wherein each carbon atom of the TCE molecule sits on top of the Pd atom. Comparing TCE adsorption over Pd facets, TCE shows the highest binding energy of -178 kJ/mol over Pd (110). TCE, upon adsorption on Pd, immediately undergoes dechlorination followed by subsequent hydrogenation of the hydrocarbon intermediates as the activation energies for C-Cl bond dissociation steps were quite low in comparison to the hydrogenation steps. As a result, the catalyst tends to undergo poisoning due to the chlorine atoms accumulated on the surface. Chlorine binds to the Pd facets as follows: Pd (110) > Pd (211) > Pd (100) > Pd (111), indicating rapid poisoning of the undercoordinated sites in comparison to the terrace site. This also suggests deactivation of smaller sized Pd nanoparticles. The strongly adsorbed Cl atoms react with hydrogen to form HCl.

Interface between metal and ceramic is assumed to be atomically sharp as mixing of anions or cations (that is part of metal and ceramic) is not expected to be thermodynamically favorable. Contrary to this belief, we establish that in Ti/TiN system, it is thermodynamically favorable for N in TiN to cross over by forming N vacancy, to Ti forming interstitial solid solution. First-principles calculated value of N vacancy formation energy in TiN is 2.17 eV and N interstitial formation in Ti is –3.84 eV. Sum of the two values, which we call as driving force indicate that mixing of anions across the Ti/TiN interface is favorable.

To explore other combinations of metal/ceramic systems that could plausibly result in chemically graded interface by mixing of anions across the interface, we calculate C, N and O vacancy formation energy in range of carbides, nitrides and oxides respectively and interstitial formation energy in metals like, Ti, Zr, Hf, V, Nb, Ta, Al, Mg, Cr, and Fe. This covers range of technologically important metal/ceramic interfaces. We find that transition metals group elements, IV B and V B are more likely to form a chemically graded interface with nitrides and carbides. However, Al₂O₃ and MgO, show a large positive vacancy formation energy, are likely to form sharp interface with any metal, which explains the reason for using them as substrates for film growth. Formation of chemically graded interface results in gradual variation of structural parameter (like lattice parameter) and properties (elastic constants) across the interface. Such chemically graded interface could lead to better properties of the heterostructure involving metal/ceramic interfaces.

LnBaCo₂O_5+d type of layered double perovskite materials have received much attention as solid
oxide fuel cell cathode materials owing to their high oxygen ion concentration, high electronic
conductivity and catalytic activity towards oxygen reduction. In the present work, Nd-based
double perovskites NdBa_1-xSr_xCo₂O_5+d (NBSCO, x= 0, 0.25 and 0.50) have been studied
computationally.
Plane wave Density functional Theory based calculations using VASP were performed in order
to examine the electrocatalytic properties of NdBa_1-xSr_xCo₂O_5+d double perovskite material. In
view of the application of NBSCO material for SOFC cathodes, the bulk oxygen vacancy
formation energies (E_ov) have been calculated computationally for oxygen vacancies created in
all possible planes (BaSr/O, Nd/O and Co/O) and surface energies (γ) of the structure with
different surface terminations (BaSr/Co, Nd/Co, Co/BaSr and Co/Nd) along (001) direction. Nd/O plane
observed to have lowest oxygen vacancy formation energy among all the three possible planes in
(001) direction of bulk NBSCO. This shows Nd/O plane to have high oxygen vacancy
concentration. For x=0, 0.25 and 0.50, BaSr/O plane have highest oxygen vacancy formation
energy showing a difficulty in oxygen vacancy creation in BaSr/O plane as compared to other
planes. This suggested less oxygen anion diffusivity in BaSr/O plane. However, on doping one
fourth and half of the Ba with Sr resulted in an improved bulk oxygen vacancy characteristic of
BaSr/O plane. Different energetics of different terminal surfaces shows importance of surface
terminations. The results of first principles calculations for surface energies were analyzed and
compared for different terminal surfaces. For NBCO material, low surface energies have been
observed for Ba/Co termination. Due to lower surface energies, Ba ions have tendencies to
segregate towards surface. This is in accordance with the DFT simulations and molecular
dynamics simulations of other Ba containing LnBaCo₂O_5+d layered perovskites [1-5]. Doping the
material with Sr have also shown similar trend in surface energies of BaSr/Co terminal surface.

References:
1. Anjum, U., Vashishtha, S., Sinha, N., & Haider, M. A. (2015). Role of oxygen anion diffusion in
improved electrochemical performance of layered perovskite LnBa_1-ySr_yCo_2-xFe_xO_5+δ(Ln=Pr, Nd, Gd)
electrodes. Solid State Ionics, 280, 24-29.
2. Anjum, U., Vashishtha, S., Agarwal, M., Tiwari, P., Sinha, N., Agrawal, A., & Haider, M. A. (2016).
Oxygen anion diffusion in double perovskite GdBaCo₂O_5+δ and LnBa_0.5Sr_0.5Co_2−xFe_xO_5+δ (Ln = Gd,
Pr, Nd) electrodes. International Journal of Hydrogen Energy, 41(18), 7631-7640
3. Anjum, U., Khan, T. S., Agarwal, M., & Haider, M. A. (2019). Identifying the Origin of the Limiting
Process in a Double Perovskite PrBa_0.5Sr_0.5Co_1.5Fe_0.5O_5+δ Thin-Film Electrode for Solid Oxide Fuel
Cells. ACS Applied Materials & Interfaces, 11(28), 25243-25253
4. Anjum, U., Agarwal, M., Khan, T. S., & Haider, M. A. (2019). Mechanistic Elucidation of Surface Cation
Segregation in Double Perovskite PrBaCo₂O_5+δ Material using MD and DFT Simulations for Solid Oxide
Fuel Cells. Ionics, 26(3), 1307–1314
5. Anjum, U., Agarwal, M., Khan, T. S., Prateek, P., Gupta, R. K., & Haider, M. A. (2019). Controlling
surface cation segregation in a nanostructured double perovskite GdBaCo₂O_5+δ electrode for solid
oxide fuel cells. Nanoscale, 11(44), 21404-21418.

Many crystalline compounds are composed of one or more structural units. When these units can be “stacked” in different ways to form stable or metastable phases, the resulting phases are known as polytypes. Among these polytypes, the crystalline systems composed of close-packed (CP) layers have especially attracted attention on their fundamental and technological properties. While these polytypes are often experimentally observed in wide-bandgap semiconductors, SiC systems are particularly known to show several hundred polytypes [1]. The long period stacking ordered (LPSO) Mg alloys with light weight, high specific strength, and high heat resistance are also recently drawing attention as a metallic system with similar polytypism to that in SiC [2, 3]. For both systems, the physical mechanism behind polytype selection is not yet fully understood.
Predicting polytype phase stability for a material has still been a long-standing issue in condensed matter physics and/or materials science. This stems from the fact that the atomistic interactions on polytype energetics might be surprisingly quite complex and delicate despite the simplicity of their geometrical structure. In this situation, some theoretical studies have recently been reported. Polytypism for the finite range Lennard-Jonesium based on the classical atomistic simulations has shown that its ground state structures can include not only fcc (3C) and hcp (2H) but a wide range of more complex stacking sequences depending on the interatomic interaction distance [4]. In addition, the enthalpy of any CP structure for a given element is recently found to be characterized as a linear expansion like a convergent series which describe the stacking configuration [5]. In the previous work, we have also presented a consideration of total energetics for the CP polytypes based on the geometrical analysis for the correlation between interlayer interactions and interatomic ones in CP polytypes [6]. These theoretical results suggest that short-range interactions are not enough to describe the CP polytype energetics and provide significant insights for creating interatomic models successfully showing the polytypes other than 3C and 2H structures as a ground state, those have never yet been implemented as far as the authors know.
Since the ground state for pure lanthanum (La) is the CP stacking structure with four layers along the c-axis in the unit cell, i.e. the double hexagonal CP structure (DHCP), the pure La can be an important reference system for studying the polytype formation. It is, therefore, possible to investigate the essential factors determining the polytype selection rule through the dynamical analyses for La. In the present work, we report on the process of constructing an interatomic potential with good descriptiveness on the La polytype energetics, that can be used for molecular dynamics (MD) simulations.
The Embedded Atom Method (EAM) type functions reported by Mishin et al. [7] are adopted for constructing the potential model in this study. Since our previous theoretical studies have shown that the long-range nature of interatomic interactions is an important factor in determining the ground state of polytype energetics [3, 6], the cutoff radius has been carefully selected considering the computational speed in MD simulations. Other basic properties and transferability of the EAM type potential constructed will be discussed in the presentation.

[1] K. Moriguchi, et al., J. Mater. Res. 28, 7 (2013).
[2] E. Abe et al., Phil. Mag. Lett, 91, 690 (2011).
[3] K. Moriguchi et al., 2020 Virtual MRS Spring/Fall Meeting & Exhibit, F.SF07.06.03 (2020) and submitted in MRS Advances.
[4] L. B. Pártay et al., , Phys. Chem. Chem. Phys.,19, 19369 (2017).
[5] C. H. Loach and G. J. Ackland, Phys. Rev. Let.119,205701 (2017).
[6] S. Ogane et al., 2020 Virtual MRS Spring/Fall Meeting & Exhibit, F.SF07.06.01 (2020) and submitted in MRS Advances.
[7] Y. Mishin et al., Phys. Rev. B 59, 3393(1999).

Polytypism is a special case of polymorphism when the two polymorphs differ only in the stacking of identical two-dimensional sheets or layers. The polytypes are characterized by a stacking sequence with a given repeat unit along the hexagonal c-axis direction and are theoretically possible to have endless permutations of the sequences. Among these polytypes, the crystalline systems composed of close-packed (CP) layers have especially attracted attention on their fundamental and technological properties for many years.
Predicting polytype phase stability for a material has still been a long-standing issue in condensed matter physics and/or materials science. This situation stems from the fact that the atomistic interactions on CP polytype energetics might be surprisingly quite complex and delicate despite the simplicity of their geometrical structure. We have proposed a computational method coupled with three theoretical tools (PGA: polytype generation algorithm; FPC-DFT: first-principles calculations based on the density functional theory; and ANNNI: axial next-nearest-neighbor Ising model), which can make us possible to efficiently investigate the structural energetics for diverse nonequivalent polytypes [1]. The equilibrium theories based on the ANNNI model that is well known in the field of statistical mechanics have played an efficient role in the study of the origins of polytypism [2, 3].
We have constructed an ANNNI model including interactions up to the third-nearest neighbor layer with four-spin term to investigate the static energetics of a wide variety of CP polytypes for 17 kinds of metallic elements in our recent work [4]. Using this ANNNI model, we can discuss phase stability of polytypes based on inter-layer interactions for the metallic systems [4]. We have also presented a theoretical consideration of total energetics for the close-packed (CP) polytypes based on the interlayer partial energy model where the total energy constructed from the two-body interatomic interactions is projected onto the interlayer interactions in CP polytype structures [5]. Our theoretical study suggests that the descriptiveness on polytype energetics changes according to the atomic interaction distance and the effective interatomic distance that controls the ground state for the polytype energetics can be inferred from the distribution of polytype structural energetics [5].
Loach and Ackland have recently proposed another convergent series lattice model on the polytype energetics where the stacking order description is different from that in the ANNNI model [6]. They emphasize that the model proposed is more useful than the classical ANNNI model since it converges more rapidly. While these theoretical results suggest that the convergent series lattice model such as the ANNNI and/or Loach's model is a powerful tool to describe the polytype energetics, the accuracy, the convergency and the physical meaning for each model have not been completely clarified and not been mutually compared with each other.
In the present work, a comparative study on convergent series lattice models for close-packed polytype energetics are carried out using both ANNNI and Loach’s models. Using these models extracted from the first-principles calculations within the generalized gradient approximation (GGA), we will discuss the inter-layer interactions, the polytype phase diagrams, and the physical relation between the ANNNI and Loach's models.

[1] K. Moriguchi, et al., J. Mater. Res. 28 7-16 (2013).
[2] E. Rodriguez-Horta et al., Acta Cryst. A73, 377 (2017).
[3] J. J. A. Shaw and V. Heine, J. Phys.: Condens. Matter 2, 4351 (1990).
[4] K. Moriguchi et al., 2020 Virtual MRS Spring/Fall Meeting & Exhibit, F.SF07.06.03 (2020) and submitted in MRS Advances.
[5] S. Ogane et al., 2020 Virtual MRS Spring/Fall Meeting & Exhibit, F.SF07.06.01 (2020) and submitted in MRS Advances.
[6] C. H. Loach and G. J. Ackland, Phys. Rev. Lett. 119, 205701 (2017).

With the discovery of new sources of natural gas, hydrocarbon products obtained from natural gas are providing a greater avenue to reduce dependence on coal and petroleum-based products. In this regard, direct conversion of methane to aromatics in non-oxidative environment is explored as an energy efficient route, as it eliminates the production of syngas and also eradicates the separation of COx from the product. For methane dehydroaromatization (MDA) reaction, Mo/HZSM-5 is widely used as the catalyst, yielding high selectivity for aromatics. Though, the catalyst is rapidly deactivated by coke formation in the form of polyaromatics hydrocarbon. And this remains an issue to be resolved. One thought to improve catalyst stability is arising from a detailed understanding of the catalytically active site which is dictating the protocols of catalyst synthesis, choice of the metal precursor, carburizing environment. Here in this work, utilizing density functional theory (DFT) calculations, we are discussing the implication of the oxycarbide species of molybdenum versus the carbide species in activating methane and formation of ethylene/acetylene intermediates. Overall, the results are highlighting the fundamental mechanistic insights on the active sight, which may provide a clue for rational catalyst design.

Electronic structure calculations, especially those using density functional theory (DFT), have been very useful in understanding and predicting a wide range of materials properties. Despite the success of DFT, and the tremendous progress in theory and numerical methods over the decades, the following challenges remain. Firstly, the state-of-the-art implementations of DFT suffer from cell-size and geometry limitations, with the widely used codes in solid state physics being limited to periodic geometries and typical simulation domains containing a few thousand electrons. This limits the complexity of materials systems that are accessible to DFT calculations. Secondly, most electronic structure calculations rely on the pseudopotential approximation, treating only the valence electrons. Recent studies have elucidated many scenarios where the pseudopotential approximation and the widely used pseudopotentials are unsatisfactory. Lastly, there are many materials systems (such as strongly-correlated systems) where the widely used model exchange-correlation functionals are inaccurate. Addressing these challenges will enable large-scale all-electron quantum-accuracy DFT calculations, and can significantly advance our predictive modeling capabilities of complex materials systems.

This talk will discuss our recent advances towards addressing the aforementioned challenges. In particular, the development of computational methods and numerical algorithms for large-scale real-space DFT calculations using adaptive finite-element discretization will be presented, which form the basis for the recently released DFT-FE open-source code. The computational efficiency, scalability and capability of DFT-FE will be presented, and contrasted with other widely used codes. In an effort to overcome the limitation of the pseudopotential approximation, recent progress in developing accurate, efficient, and scalable all-electron DFT calculations will be presented. Further, ongoing efforts, and related thoughts, on developing a framework for a data-driven approach to improve the exchange-correlation description in DFT will be discussed.

The use of Ab initio methods to address problems in chemical and material sciences (CMS) which are solved using classical computation is a mature and robust field. With the nascent field of quantum computing (QC) anticipated to grow and make advancements in the upcoming decades, now is a suitable time to investigate quantum algorithms and methodologies that positively augment or advance Ab initio calculations. We present a brief overview of leading quantum algorithms for noisy intermediate-scale quantum devices that target CMS problems, which include the successful variational quantum eigensolver (VQE). We discuss our two recent QC approaches for calculation of both ground and excited states. The first of these methods utilizes a subspace projection of a problem Hamiltonian in conjunction with the VQE algorithm to obtain the excited states accurately. The second method utilizes a quantum device to prepare and measure an effective Hamiltonian in the computational basis of a qubit register. In this capacity, the quantum device acts as a coprocessor that can efficiently prepare the Hamiltonian for post-processing on a classical computer. The methods discussed are numerically demonstrated for small molecular systems (e.g., H₂, LiH), but in general, are suitable for larger chemical or material systems with appropriate quantum hardware resources. While mainstream QC may still be far away, we are at an opportunistic intersection for the materials community to think about how to address CMS problems using computing devices governed by quantum theory.

Acknowledgment: This material is based upon work supported by General Atomics internal R&D funding.

Computationally tractable treatment of correlated quantum matter is a challenging problem relevant to chemistry, physics, and material science. It has been predicted that quantum computers have the potential to reduce the computational scaling from exponential to polynomial, however, environmental noise experienced by these devices has stymied the practical realization of this speed-up. With recent progress in quantum hardware, quantum devices are closer than ever to being capable of computationally investigating static and dynamic properties of strongly correlated systems. Here, I will discuss recently developed quantum algorithms to consider strongly correlated quantum systems. In particular I will focus on the dynamics of fermionic open quantum systems and static properties of condensed matter systems.

By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semi-local density functional theory (DFT), and thereby furnish a more accurate and reliable description of the electronic structure in systems throughout chemistry, physics, and materials science. However, the high computational cost associated with hybrid DFT limits its applicability when treating large-scale and complex condensed-phase systems. To overcome this limitation, we have devised a highly accurate and linear-scaling (order-N) approach based on a local (MLWF) representation of the occupied space that exploits sparsity when evaluating the EXX interaction in real space [1]. In this work, we present a detailed description of the theoretical and algorithmic advances that are needed to perform hybrid DFT based ab initio molecular dynamics (AIMD) simulations of large-scale finite-gap condensed-phase systems using this approach. This is followed by a critical assessment of the accuracy and parallel performance of the exx algorithm when performing AIMD simulations of liquid water and several ice phases in the canonical (NVT) and isobaric-isothermal (NpT) ensembles. With access to high-performance computing (HPC) resources, we demonstrate that exx enables hybrid DFT based AIMD simulations of systems containing 500-1000 atoms with a wall time cost comparable to semi-local DFT. In the strong-scaling limit, this cost is split evenly between computation, communication, and processor idling; as such, we also discuss a three-pronged strategy that directly attacks each of these contributions and reduces the overall wall time cost by approximately an order of magnitude for large-scale heterogeneous systems. With these developments, this work takes us one step closer to routinely performing AIMD simulations of large-scale condensed-phase systems for sufficiently long timescales at the hybrid DFT level.

[1] J Chem Theory Comput 16, 3757 (2020).

Studying the metal-insulator transition (MIT) of VO₂ from first-principles generally requires the use of computationally expensive hybrid density functionals, while the less resource-intense functionals of the generalized gradient approximation (GGA) -type commonly fail to correctly describe the relative thermodynamic stabilities, crystal-, or electronic structures of the semiconducting and metallic monoclinic and rutile phases of VO₂. Unfortunately, investigating e.g. the effect of low-concentration doping on the VO₂ transition temperature requires simulation cell dimensions for which hybrid density functionals quickly become unfeasible. We present an overview of the underlying difficulties connected to the use of GGA functionals on the VO₂ MIT in commonly employed quantum chemistry codes and demonstrate that a computational setup using localized basis functions, pseudopotentials and a GGA functional with a small Hubbard correction helps achieving simultaneous description of qualitative band structure features, crystal geometries, and the MIT temperature of VO₂ correctly.

We review recent advances towards first-principles quantum monte carlo (QMC) on general materials, including those where spin-orbital phenomena, strong electron correlation, and van der Waals interactions are significant. QMC methods provide very high accuracy and are in principle generally applicable. However fundamental improvements are required to study quantum materials as well as general materials incorporating elements from across the periodic table. Additionally, QMC methods generally make use of trial wavefunctions from other approximate theories to control the Fermion sign problem, introducing a systematic bias to the calcualtions. For simple bulk materials these trial wavefunctions can now be converged and the systematic error reduced[1,2]. This can accelerate methodological improvements by enabling cross validation and studies of the efficiencies of different QMC methods such as real space diffusion QMC and auxiliary field QMC. In terms of applications, these advances open the possibility to determining the total uncertainty in predicted properties of both quantum and general materials.

The methods described have been implemented in the open source QMCPACK code[3,4], https://qmcpack.org .

[1] F. Malone et al. “Systematic comparison and cross-validation of fixed-node diffusion Monte Carlo and phaseless auxiliary-field quantum Monte Carlo in solids”, Phys. Rev. B 102, 161104(R) (2020). https://doi.org/10.1103/PhysRevB.102.161104
[2] A. Benali et al. “Towards a Systematic Improvement of the Fixed-Node Approximation in Diffusion Monte Carlo for Solids”, Accepted in J. Chem. Phys. (2020). https://arxiv.org/abs/2007.11673
[3] P. Kent et al. “QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion quantum Monte Carlo”, J. Chem. Phys. 152 174105 (2020). https://doi.org/10.1063/5.0004860
[4] J. Kim et al. “QMCPACK: an open source ab initio quantum Monte Carlo package for the electronic structure of atoms, molecules and solids” J. Phys.: Condens. Matter 30 195901 (2018). https://doi.org/10.1088/1361-648X/aab9c3

The recently introduced topological quantum chemistry (TQC) framework has provided a description of universal topological properties of all possible band insulators in all space groups based on crystalline unitary symmetries and time reversal. While this formalism filled the gap between the mathematical classification and the practical diagnosis of topological materials, an obvious limitation is that it only applies to weakly interacting systems-which can be described within band theory. It is an open question to which extent this formalism can be generalized to correlated systems that can exhibit symmetry protected topological phases which are not adiabatically connected to any band insulator. In this work we address the many facettes of this question by considering the specific example of a Hubbard diamond chain. This model features a Mott insulator, a trivial insulating phase and an obstructed atomic limit phase. Here we discuss the nature of the Mott insulator and determine the phase diagram and topology of the interacting model with infinite density matrix renormalization group calculations, variational Monte Carlo simulations and with many-body topological invariants. We then proceed by considering a generalization of the TQC formalism to Green's functions combined with the concept of topological Hamiltonian to identify the topological nature of the phases, using cluster perturbation theory to calculate the Green's functions. The results are benchmarked with the above determined phase diagram and we discuss the applicability and limitations of the approach and its possible extensions.

The current most popular computational method in modelling surface reactions is periodic planewave density functional theory (DFT)¹. Periodic DFT is both expansive in its functionality, and easy to use. However, there are still some major limitations. For instance, the preferred basis representation of planewaves is inefficient for high-level hybrid-DFT approaches; large models are needed for isolated catalytic chemistry, with many tens or hundreds of atoms included but redundant in calculations, as all atoms need to be treated quantum mechanically, even if they are far from the “active site”. In addition, periodic surface models cannot be used to model charged defects due to technical incompatibilities when trying to include any compensating background charge.
As an alternative, hybrid quantum- and molecular-mechanical (QM/MM) modelling can be coupled with an embedded cluster approach, which combines the high accuracy of QM modelling, with the high efficiency of MM modelling (MM), all in an aperiodic model that reproduces the bulk environment². However, the uptake of QM/MM in the solid-state community is limited by the bespoke nature of the model configuration, which typically requires empirical tuning to achieve accuracy comparable to the periodic DFT approaches.
In this work, we present our progress in outlining systematic design principles for QM/MM models, based initially on work using MgO. This has been pursued using the ChemShell³ software package, with FHI-aims⁴ used to perform DFT calculations, using both popular GGA approaches, compared to periodic DFT, and high-level exchange-correlation functionals (PBE0).
The focus of the work is understanding how cluster design principles, such as partitioning of the QM-region, determining coordinates of the unrelaxed cluster, and fixing different regions of the cluster during relaxation, affect the accuracy of measurable results. Our overall aim is to deliver an automated approach to cluster construction, with objective justification for each step involved.

¹ Becke, J. Chem. Phys. 140, 18A301 (2014)
² Groenhof, Methods in Molecular Biology, Ch.3 (2013)
³ Sherwood et al., J. Mol. Struct. (Theochem.) 632, 1 (2003)
⁴ Blum et al., Computer Physics Communications 180, 2175-2196 (2009)

Coupled cluster theory is usually viewed as a molecular theory, but I will describe its extension to treat spectra in materials, finite-temperature and non-equilibrium effects, and electron-phonon coupling.

While Kohn-Sham density functional theory (DFT) using GGA, meta-GGA functional approximations has been remarkably successful in a variety of applications, there are several important cases where it fails. Increasingly, this is being remedied by semi-empirical DFT+U or hybrid functional calculations where parameters are adjusted in one way or another to obtain acceptable results. A variational and self-consistent implementation of the Perdew-Zunger self-interaction correction (PZ-SIC) using complex optimal orbitals has instead been developed and applied to several such systems and found to give good results. Calculations of electronic holes in oxide crystals, transition metal clusters, Rydberg excited states and localized charge state that are absent in GGA and meta-GGA level calculations will be presented. The computational effort of the PZ-SIC calculations scales with system size in the same way as DFT/GGA calculations but the prefactor is large since an effective potential needs to be evaluated for each orbital (calculations that could, however, be carried out in parallel) and optimal orbitals need to be found in terms of the Kohn-Sham orbitals at each iteration. PZ-SIC is an example of an extended functional form where the energy depends explicitly on the orbital densities, not just the total electron density and thereby goes beyond Kohn-Sham DFT. While significant improvements are obtained with PZ-SIC, the orbital density dependent functional form could be exploited more generally to develop a self-interaction free functional rather than as a correction to Kohn-Sham functionals, thereby providing an optimal mean field theory for materials calculations.

This lecture will describe theoretical aspects of spin-related phenomena in the context of novel molecular materials. Examples include spin-forbidden processes, which play an important role in photovoltaics, and molecular magnetism, which is of interest for quantum information science. Recent methodological developments within equation-of-motion coupled cluster theory will be discussed and illustrated by examples relevant to the design of novel materials.

The phase diagram of numerous materials of technological importance features high-symmetry high temperature phases that exhibit phonon instabilities. Leading examples include shape-memory alloys, as well as ferroelectric, refractory, and structural materials. In this talk I will introduce a new thermodynamic model for free energy calculation in these phases from first principles [1]. This model efficiently explores the system’s ab-initio energy surface by partitioning it into piecewise polynomials around local minima, which is combined with a continuous yet constrained sampling in the vicinity of these local minima. I present the application of this model to the bcc phase of titanium as well as the austenite and martensite phases in NiTi and PtTi shape memory alloys, in which we illustrate that constant anharmonicity-driven hopping between local low-symmetry distortions stabilizes the system to maintain a high-symmetry time-averaged structure [2]. In addition, I will try to shed light on diffusion kinetics in dynamically stabilized phases based on a first-principles approach within the transition state theory [4]. Finally, I introduce the implementation of the model as an open-access and fully automated software toolkit called the Piecewise Polynomial Potential Partitioning (P4), which can be integrated into the Alloy Theoretic Automated Toolkit (ATAT)[3].

References
[1] S. Kadkhodaei, Q.-J. Hong, and A. van de Walle, “Free energy calculation of mechanically unstable but dynamically stabilized bcc titanium,” Phys. Rev. B, vol. 95, no. 6, p. 064101, Feb. 2017.
[2] S. Kadkhodaei and A. van de Walle, “First-principles calculations of thermal properties of the mechanically unstable phases of the PtTi and NiTi shape memory alloys,” Acta Mater., vol. 147, pp. 296–303, Apr. 2018.
[3] S. Kadkhodaei and A. van de Walle, “Software tools for thermodynamic calculation of mechanically unstable phases from first-principles data,” Comput. Phys. Commun., vol. 246, p. 106712, Jan. 2020.
[4] S. Kadkhodaei and A. Davariashtiyani, "Phonon-assisted diffusion in bcc phase of titanium and zirconium from first principles" Phys. Rev. Materials 4, 043802, April 2020

Designing new quantum materials with long-lived electron spin states is in urgent need of a general theoretical formalism and computational technique to reliably predict spin lifetimes. We present a new, universal first-principles methodology based on density matrix (DM) dynamics for open quantum systems to calculate the spin-phonon relaxation time of solids with arbitrary spin mixing and crystal symmetry. In particular, this method describes contributions of the Elliott-Yafet (EY) and D’yakonov-Perel’ (DP) mechanisms to spin relaxation, corresponding to systems with and without inversion symmetry, on an equal footing[1]. Our ab initio predictions are in excellent agreement with experimental spin lifetime for a broad range of materials, such as Si, Fe, MoS₂, graphene and its interfaces as well as GaAs.

We then implemented real-time DM dynamics for ultrafast Kerr rotation and studied spin dynamics under external electric and magnetic field. Through the complete theoretical descriptions of pump, probe and scattering processes including electron-phonon, electron-impurity and electron-electron scattering, our method can directly simulate the nonequilibrium ultrafast pump-probe measurements for coupled spin and electron dynamics and is applicable to any temperatures and doping levels. We use this method to simulate spin dynamics of GaAs and obtain excellent agreement with experiments. It is found that the relative contributions of different scattering mechanisms and phonon modes vary considerably between spin and carrier relaxation processes. Importantly, we point out that at low temperatures the electron-electron scattering becomes very important and causes the strong reduction of spin relaxation time under in-plane magnetic fields.

In addition, we will also introduce our recent work on radiative and nonradiative exciton recombination in two-dimensional systems from many-body perturbation theory and its applications on designing point defects as single photon emitter and spin qubits in hexagonal BN[2-6]. Our work underscores the predictive power of first-principles techniques for key physical properties to quantum information science.

References:
[1] J. Xu, A. Habib, S. Kumar, F. Wu, R. Sundararaman, and Y. Ping, Nature Communications, 11, 2780, (2020)
[2] F. Wu, T. Smart, J. Xu, Y. Ping, Physical Review B, 100, 081407(R) (2019)
[3] F. Wu, D. Rocca and Y. Ping, Journal of Materials Chemistry C, 7, 12891, (2019)
[4] F. Wu, A. Galatas, R. Sundararaman, D. Rocca, and Y. Ping, Physical Review Materials, 1, 071001(R), (2017).
[5] T. Smart, F. Wu, M. Govoni and Y. Ping, Physical Review Materials, 2, 124002, (2018).
[6] T. Smart, K. Li, J. Xu, Y. Ping, under review, arXiv:2009.02830, (2020)

The dipole-dipole contribution to the total energy and potential due to unpaired electron spin is the magnetostatic analogue to the Hartree electrostatic term. It contributes at order 1/c² in the Breit-Pauli Hamiltonian and is therefore neglected in both non-relativistic spin-density functional theory (DFT) and non-collinear DFT calculations including spin-orbit. The term is technologically important, however, since it induces the shape anisotropy effect critical in the design of nanoscale magnetic devices; in and of itself, the term perhaps warrants investigation as an intriguing physical phenomenon.

In this work, we develop a practical algorithm for non-self-consistent but non-perturbative calculations of the spin dipole-dipole correction to the total energy in periodic and molecular systems [1]. To this end, we make use of an auxiliary—and, ultimately, physically fictitious—magnetic charge density, determined via the magnetization intrinsic to the collinear (or non-collinear) spin-density associated with ground-state systems with vanishing free current density. The affiliated magnetic scalar potential is defined by means of a magnetic Poisson equation, and from this the magnetic field is calculated. Immersing the magnetization back into this magnetic field generates the non-self-consistent energy correction.

We developed a versatile module, compatible with the capacities of Mathematica, for calculating this energy for spin-densities in generalized periodic unit cells, to be used as a post-processing tool with any standard DFT code. Using this, we compared the strength of the magnetostatic energy to the electrostatic energy for a number of test systems, finding a ratio consistently on the order of the square of the fine structure constant, as is coherent with the term’s position in the relativistic expansion. Our approach may highlight the magnetic charge density’s aptitude both as an auxiliary for computing the properties of magnetic quantum systems and, more generally, for inclusion in the development of exchange-correlation functionals in relativistic DFT.

[1] L. MacEnulty and D. D. O’Regan, Journal of Undergraduate Reports in Physics 30, 100005 (2020), DOI: 10.1063/10.0002045.

This research was funded by Science Foundation Ireland (SFI) through the Advanced Materials and Bioengineering Research Centre (AMBER, Grant No. 12/RC/2278).

The antiperovskite family Mn₃AN (A = Zn, Cu, Ni, ..) exhibits negative thermal expansion, piezomagnetism, and non-collinear antiferromagnetism (AFM) due to the presence of magnetic frustration on the magnetic structure of the manganese atoms in the (111) planes [1]. Previous research on this material has been mostly focused on experimental findings, and it has dedicated primarily on understanding the magneto-structural properties of these antiperovskites. Interestingly, we found few theoretical studies devoted to elucidate the influence of the central anionic site in the Mn₃NiN antiperovskite. Therefore, our study focuses on theoretically investigating, through first-principles density functional theory (DFT) calculations, the effect of the nitrogen’s site on the structural and electronic properties of the antiperovskites Mn₃NiN. Therefore, our main analysis consists of observing changes in the electronic structure by analyzing the band structure, density of states, and the oxidation state of the atoms in the presence and absence of nitrogen considering the allowed four noncollinear antiferromagnetic orderings. Our results show a tangible modification of the electronic structure close to the Fermi energy as well as structural changes, associated to the lattice parameter, due to the incorporation of nitrogen.

[1] Y. Wang, H. Zhang, J. Zhu, X. Lü, S. Li, R. Zou, and Y. Zhao, “Antiperovskites with exceptional functionalities,” Advanced Materials, vol. 32, no. 1905007, p. 7, 2019.

The manganese-based antiperovskite nitrides family is formed by magnetic materials that exhibit non-collinear antiferromagnetism in the presence of magnetic frustration. Different reports have confirmed the existence of a strong coupling between the magnetic structure and the crystalline structure in the in members of this family, for example in Mn₃NiN. As such, this coupling has been confirmed by piezomagnetism [1], magnetovolume effects [2], and negative thermal expansion [3] studies.

So far, theoretical studies focused on clarifying this coupling and phenomenon in antiperovskites are rare in the literature. This possibly because phonon calculations, including non-collinear magnetism formalism are a challenging task in these type systems. In this research, we theoretically studied the spin-phonon coupling in Mn₃NiN through first-principle DFT calculations. We aimed to understand the relation between the behavior of the phonons and the magnetic orderings of the material, taking into consideration correlation effects. To achieve this, we computed and analyzed the phonon frequencies, eigenvectors, and phonon dispersion curves for each of the two magnetic orderings that have been experimentally confirmed in the material [4]. From these results the phonon modes involved in the coupling were determined. Our results theoretically demonstrate the dependence of phonons on magnetic ordering and correlation effects in Mn₃NiN. With this study, we expect to contribute to future research in the field of antiperovskites that display a coupling between structure and magnetism.

[1] D. Boldrin, A. P. Mihai, B. Zou, J. Zemen, R. Thompson, E. Ware, B. V. Neamtu, L. Ghivelder, B. Esser, D. W. McComb, et al., “Giant piezomagnetism in Mn3NiN,” ACS applied materials & interfaces, vol. 10, no. 22, p. 18863, 2018.

[2] K. Takenaka, M. Ichigo, T. Hamada, A. Ozawa, T. Shibayama, T. Inagaki, and K. Asano, “Magnetovolume effects in manganese nitrides with antiperovskite structure,” Science and technology of advanced materials, vol. 15, no. 1, p. 1, 2014.

[3] M. Wu, C. Wang, Y. Sun, L. Chu, J. Yan, D. Chen, Q. Huang, and J. W. Lynn, “Magnetic structure and lattice contraction in Mn3NiN,” Journal of Applied Physics, vol. 114, no. 12, p. 123902, 2013.

[4] D. Fruchart and E. F. Bertaut, “Magnetic studies of the metallic perovskite-type compounds of manganese,” Journal of the physical society of Japan, vol. 44, no. 3, p. 781, 1978.